1. Field of the Invention
This invention relates generally to data converters, and more particularly to a system and method for correcting the beta mismatch between thermometer encoded and R-2R ladder segments of a current steering digital-to-analog converter (DAC).
2. Description of the Prior Art
The technique of segmentation has been used, among other reasons, to reduce both the area and power consumption of digital-to-analog converters (DACs). Each segment generally uses either a binary-to-thermometer encoder or a binary-to-binary encoder. For an N-bit current steering DAC, there is a desire to combine an M-bit thermometer encoded segment with an L-bit binary encoded segment. In this notation, the M-bit segment represents the most significant bits (MSBs), and the L-bit segment represents the least significant bits of the N-bit DAC, where N=M+L. FIG. 1 illustrates a block diagram of an N-bit current steering DAC 100.
The M-bit thermometer encoded segment 102 of the DAC 100 as shown in FIG. 1 consists of 2Mxe2x88x921 equal current sources 104. These current sources 104 are individually switched to either the true or complement output as determined by the thermometer encoding of the M most significant bits. Also shown in FIG. 1 is a binary encoded L-bit segment 106 of the DAC 100 as an R-2R ladder. The R-2R ladder outputs a binary weighted current to the true or complement output as determined by the L least significant bits of the N-bit input.
The foregoing DAC 100 has a boundary condition between the MSB and the LSB segments that must be satisfied for the DAC 100 output to remain linear. This boundary condition necessitates that the total output current of the R-2R ladder must be one least significant bit less than the output current of a single current source in the MSB segment. This condition is met to first order by using a replica MSB current source 108 to supply the total current to the R-2R ladder where it is noted that the R-2R circuit already functions to subtract the equivalent of an LSB current from the total current supplied. The replica MSB current source 108 is labeled IREP in FIG. 1.
According to one embodiment, the foregoing boundary condition requiring the DAC 100 to remain linear across the two segments 102, 106 is only met to first order because the NPN devices used throughout have a current gain, xcex2F, that is dependent on the collector current density. This will cause the total base current of the R-2R ladder to not equal that of the cascode of an MSB unit current source and result in a nonlinearity. This concept can be better understood by taking a closer look at the M-bit thermometer encoded segment 102 MSB current source 104 and the binary encoded L-bit segment 106 R-2R ladder designs.
One embodiment of a current source 200 that can be used in the MSB segment 102 is shown in FIG. 2. The current source 200 consists of a bipolar junction transistor (BJT) 202 designated as Q1, a degeneration resistor 204, designated as RE, a cascode device 206, designated as Qc, and a differential output switch 208, consisting of transistors 210 and 212, designated as QSWxe2x80x94MSB and Q{overscore (SWxe2x80x94MSB)} respectively.
One embodiment of the LSB segment circuit 106 which includes the R-2R ladder 300 is shown in FIG. 3. The LSB segment circuit 106 consists of a BJT 302, designated as Q1r, and degeneration resistor 304, designated as REr, where the subscript r denotes the devices to be replicas to those in the MSB current source 200 described herein before with reference to FIG. 2. The R-2R ladder 300 consists of L binary weighted currents that are established with a binary weighted number of BJT devices 306 (Qbi). Here, the notation b represents the significance of the current from 1 to L, and i represents the NPN device within that current from 1 to 2bxe2x88x921. For example, the LSB device 308 has a b=1 and NPN devices indexed from 1 to 20=1. The most significant current weight in the R-2R ladder 300 has a b=L and NPN devices indexed from i=1 to i=2Lxe2x88x921. Also shown in FIG. 3 is an output switch for each binary weighted current. These output switches 310 are identical to those of the MSB segment 200 described in FIG. 2.
It can be seen from FIG. 3 that the R-2R ladder 300 in the LSB segment 106 is substituted for a single cascode device of an MSB unit current source. Further, the LSB segment 106 has L output switches 310 (differential pairs) and one dump device 320 (Qd), compared with the MSB unit current source that has just one output switch. The boundary condition, discussed herein before, requires the total output current of the LSB segment 106 to be one LSB less than that supplied to the output by an MSB unit. This boundary condition requires that the total base current of the R-2R ladder 300 NPN devices 306, xcexa3IB(Qbi), L output switches 310, IB(QSWxe2x80x94LSB), and dump device 320, IB(Qd), should be equal to the total base current of the MSB unit cascode 206, IB(Qc), and the output switch 208, IB(QSWxe2x80x94MSB). This boundary condition is described by equation (1) below as:                                                                         ∑                                  xe2x80x83                                                            b                =                1                            L                        ⁢                          xe2x80x83                        ⁢                          (                                                                    ∑                                          i                      =                      1                                                              2                                              b                        -                        1                                                                              ⁢                                      xe2x80x83                                    ⁢                                                            I                      B                                        ⁡                                          (                                              Q                        bi                                            )                                                                      +                                                      I                    B                                    ⁡                                      (                                          Q                      SW_LSB                                        )                                                              )                                +                                    I              B                        ⁡                          (                              Q                d                            )                                      =                                            I              B                        ⁡                          (                              Q                c                            )                                +                                    I              B                        ⁡                          (                              Q                SW_MSB                            )                                                          (        1        )            
The boundary condition of equation (1) however is not satisfied since the NPN current gain, xcex2F, has a dependence on collector current density. A typical plot of current gain as a function of collector current is illustrated in FIG. 4. The collector current density of an MSB unit current source which uses a minimum feature size cascode device 206 is in the range of 400 xcexcA/xcexcm2. This same current density will be present in the MSB 20 unit output switch 208 as well.
With continued reference to FIG. 4, it can be seen that the current gain, xcex2F, at a 400 xcexcA/xcexcm2 current density is approximately 87 A/A. The collector current density for an L=4 bit R-2R ladder is approximately 27 xcexcA/m2 or a factor of 16 less. FIG. 4 shows that this lower current density corresponds to a current gain of 92 A/A or an increase of 6%. This 6% difference in current gain, xcex2F, will cause the total base current in the R-2R ladder to be 6% less than the cascode device 206 of an MSB unit since IC=xcex2FIB. A 6% error at the boundary of an L=4 bit segment will translate into a differential nonlinearity with a magnitude approximately equal to one LSB (i.e. 24*0.06=0.96) and repeats every 16 codes.
Adding to the differences between the R-2R ladder and the cascode device 206 are the different current densities associated with the output switches 208, 310. Since the MSB unit current source 200 uses an output switch NPN of size equal to the cascode device 206, the current density will be the same 400 xcexcA/xcexcm2. The effective current density of the output switches 310 in the LSB segment 106 however, will be (400 xcexcA/xcexcm2)/L. For an LSB segment of L=4, the current density will be 100 xcexcA/xcexcm2 and the current gain will be 90. This is a smaller error of 3%; however, this will correspond to a differential nonlinearity having a magnitude of 0.5 LSB.
The above described effective base current mismatches between an MSB unit and the LSB segment 106 are additive and will result in a differential nonlinearity of approximately 1.5 LSBs that repeat every 2L codes in the DAC 100 transfer function. This error is present even with a perfect R-2R ladder and no mismatch between a MSB unit and replica current source. Further, the magnitude of this error increases with L.
In view of the foregoing, there is a need for a system and method for eliminating the differential nonlinearities caused by beta mismatches between thermometer encoded and R-2R ladder segments of a current steering digital-to-analog converter (DAC).
The present invention provides a system and method for eliminating the differential nonlinearity caused by beta mismatches between thermometer encoded (MSB) and R-2R ladder (LSB) segments of a current steering digital-to-analog converter (DAC).
In one aspect of the invention, a system is provided that creates a correction current equal to the difference in base current between a thermometer encoded and a binary encoded segment of a DAC.
In another aspect of the invention, a system is provided that creates a correction current for any combination of M-bits with a most significant bit segment and an L-bit least significant bit segment of a DAC, where N=M+L is the total number of bits in the DAC.
In still another aspect of the invention, a system is provided for subtracting a correction current from the current supplied to the LSB segment R-2R ladder circuit of a DAC.
According to one embodiment of the present invention, a circuit consists of three replica MSB unit current sources, I1, I2 and I3. The replica current II acts as a replica to a cascode device of the MSB unit of a current steering DAC. The replica current I2 replicates an effective base current equal to the total base current in the R-2R ladder circuit portion of the current steering DAC. The replica current I3 replicates the total base current of the L output switches in the LSB segment of the current steering DAC. A high impedance summing node produces a correction current ICOR=I1xe2x88x92(I2+I3). This current is equal to the current difference between an MSB unit and the LSB segment. This correction current is then subtracted from the MSB unit current source that supplies current into the R-2R ladder such that the current supplied to the R-2R ladder will be equal to the MSB replica current source minus the correction current.